Watching a James Bond movie, I noticed James gets shot, winces a little and continues on as normal, bleeding and all. Is that plausible? Later in in the movie, he gets shot again, falls unconscious onto a river and survives with recovery. I’ve never been shot but I’d imagine that even if my body is pumping adrenaline, I would be in pain. Is there such thing as “getting used” to getting shot to the point where you can just carry on after an injury? I suppose it also depends on where you got shot.

No, or at least not through that logic.
You don’t build up a tolerance for getting shot, but people can, and do, keep
fighting through gunshot wounds.

It’s fairly common for someone to not
realize they’ve been shot. Adrenaline actually deadens the sensation of pain,
and so they’ll take a bullet, then begin feeling fatigue as they bleed to death
and, eventually collapse. In situations where the bullet missed hitting
anything vital, and the actual bloodloss is slow, they can remain functional
for quite some time. This is one of the reasons you’ll frequently see
characters checking themselves for injuries after a fight. This is also one of
the reasons why you’ll see “professional” characters firing multiple shots in
quick succession. It’s not that one bullet won’t get the job done, it’s that
depending on where it hits, a single wound won’t stop their foe.

Even in situations where the bullet
damages vital internal organs, like the lungs, it’s sometimes possible the
victim still won’t realize they’ve been hit until after the fact. Ironically,
this can include headshots, which are only lethal about 98% of the time.

So, getting shot, or hit by shrapnel, is
something that you can, absolutely, keep fighting through. It’s not that you’re
dealing with a character who’s so badass they can go through the pain, it’s
that in most cases they do not know they’ve been hit. If there is an
unrealistic element to this, it’s that Bond felt the hit, and responded to it, not
that he could keep fighting afterwards.